Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
• (Section 4.2) For a given temperature T, find the wavelength at which blackbody radiation is most intense; that is, find the value of λ for which the Planck function (4.28) is maximum. Show that λmax ∝ 1/T, a result called Wien’s displacement law (“displacement” because it specifies how λmax moves with temperature). (This is surprisingly hard. It may help to rewrite I(λ, T) in terms of the variable x = hc/λkBT, and then find the value of x where I is maximum. This will lead you to a transcendental equation for x, which you can solve only with a computer. Some software can solve an equation of the form f(x) = 0 automatically, but you can also solve it graphically (to any desired accuracy) by making a plot of f(x) and zooming in on the neighborhood of the zero.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.